Question

How do you write the expression `(root3(3a))^4` in exponential form?

Answer 1

See the entire solution process below:

Explanation:

First, use this rule of exponents and radicals to put the term within the parenthesis in exponential form:

`root(color(red)(n))(x) = x^(1/color(red)(n))`

`(root(color(red)(3))(3a))^4 = ((3a)^(1/color(red)(3)))^4`

Now, use this rule of exponents to combine the exponents inside and outside the parenthesis:

`(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`((3a)^color(red)(1/3))^color(blue)(4) = (3a)^(color(red)(1/3) xx color(blue)(4)) = (3a)^(4/3)`